Question

determine a series of transformations that would map figure t onto figure u. press \try\ to test a transformation or sequence of transformations. a rotation of 180° clockwise about the origin followed by a rotation 90° counterclockwise about the origin.

Explanation:

Step1: Analyze the rotation of \(180^{\circ}\) clockwise

A \(180^{\circ}\) clockwise rotation about the origin changes the coordinates \((x,y)\) to \((-x,-y)\).

Step2: Analyze the rotation of \(90^{\circ}\) counter - clockwise

A \(90^{\circ}\) counter - clockwise rotation about the origin changes the coordinates \((x,y)\) to \((-y,x)\).

Combining these two rotations: First, perform \(180^{\circ}\) clockwise rotation \((x,y)\to(-x,-y)\), then perform \(90^{\circ}\) counter - clockwise rotation \((-x,-y)\to(y, - x)\)

Another way: We know that the composition of a \(180^{\circ}\) clockwise rotation and a \(90^{\circ}\) counter - clockwise rotation is equivalent to a \(270^{\circ}\) clockwise rotation. But if we consider the order of operations as given in the problem (first \(180^{\circ}\) clockwise then \(90^{\circ}\) counter - clockwise)

Answer:

A rotation of \(180^{\circ}\) clockwise about the origin followed by a rotation of \(90^{\circ}\) counter - clockwise about the origin.